A square shaped well has to be dug. Cost of the land is 1800 rupee per square feet and cost of diggi

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13 Oct 2011 well

A square shaped well has to be dug. Cost of the land is 1800 rupee per square feet and cost of digging (based on depth) is 500 rupee per feet. The cost of digging is not based on area of the plot. We have to make a well of 1000 cubic feet volume. What will be its dimensions (in feet) for minimum cost.

OPtion

1) (50/9)^1/2, (50/9)^1/2, 180
2) 20, 20, 2.5
3) 10, 10, 10
4) (50/3)^1/2, (50/3)^1/2, 60
5) (100/3)^1/2, (100/3)^1/2, 30
6) (25/6)^1/2, (25/6)^1/2, 240
7) 5, 5, 40
8) (25/3)^1/2, (25/3)^1/2, 120
9) 12, 12, 125/18
10) none of these

Solution

According to given condition cost = 1800*(x^2)+500*h, and (x^2)*h=1000
cost will be minimum if 1800*(x^2) = 500*h
so 1800*(1000/h)=500*h so h^2=1800*1000/500=3600 so h^2=3600 or h=60feet
so 4th option is correct

Correct Option: 4 Best Solution (0)